3/4x-10=x+1

Solution for 3/4x-10=x+1 equation:

3/4x-10=x+1

We move all terms to the left:

3/4x-10-(x+1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-x-1-10=0

We multiply all the terms by the denominator


-x*4x-1*4x-10*4x+3=0

Wy multiply elements

-4x^2-4x-40x+3=0

We add all the numbers together, and all the variables

-4x^2-44x+3=0

a = -4; b = -44; c = +3;
Δ = b2-4ac
Δ = -442-4·(-4)·3
Δ = 1984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-8\sqrt{31}}{2*-4}=\frac{44-8\sqrt{31}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+8\sqrt{31}}{2*-4}=\frac{44+8\sqrt{31}}{-8}
$